OSA's Digital Library

Applied Optics

Applied Optics


  • Vol. 42, Iss. 1 — Jan. 1, 2003
  • pp: 71–90

Analytical modeling of the white-light fringe

Slava G. Turyshev  »View Author Affiliations

Applied Optics, Vol. 42, Issue 1, pp. 71-90 (2003)

View Full Text Article

Enhanced HTML    Acrobat PDF (282 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



An analytical technique for extracting phase, visibility, and amplitude information as needed for interferometric astrometry for the Space Interferometry Mission (SIM) is presented. This model accounts for a number of physical and instrumental effects and is valid for the general case of a bandpass filter. I was able to obtain a general solution for polychromatic phasors and to address the properties of unbiased fringe estimators in the presence of noise. For demonstration purposes I studied a rectangular bandpass filter with two different methods of optical path difference (OPD) modulation: stepping and ramping OPD modulation. A number of areas for further studies relevant to instrument design and simulations are outlined and discussed.

© 2003 Optical Society of America

OCIS Codes
(120.2440) Instrumentation, measurement, and metrology : Filters
(120.2650) Instrumentation, measurement, and metrology : Fringe analysis
(120.3180) Instrumentation, measurement, and metrology : Interferometry
(120.5050) Instrumentation, measurement, and metrology : Phase measurement
(120.5060) Instrumentation, measurement, and metrology : Phase modulation

Original Manuscript: June 5, 2002
Revised Manuscript: September 24, 2002
Published: January 1, 2003

Slava G. Turyshev, "Analytical modeling of the white-light fringe," Appl. Opt. 42, 71-90 (2003)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. R. Danner, S. C. Unwin, eds., SIM Interferometry Mission: Taking the Measure of the Universe, NASA Doc. JPL 400-811 (NASA, Washington, D.C., 1999).
  2. S. C. Unwin, S. G. Turyshev, eds., Science with the Space Interferometry Mission, JPL Publ. 02-01 (Jet Propulsion Laboratory, Pasadena, Calif., 2002); see also http://sim.jpl.nasa.gov/ .
  3. A. Quirrenbach, D. Mozurkewich, D. F. Buscher, C. A. Hummel, J. T. Armstrong, “Phase-referenced visibility averaging in optical long-baseline interferometry,” Astron. Astrophys. 286, 1019–1027 (1994).
  4. S. G. Turyshev, “Analytic expressions for the while light fringe extraction,” JPL Internal Tech. Memo. 00-0901 (Jet Propulsion Laboratory, Pasadena, Calif., 2000).
  5. M. Milman, S. Basinger, “Error sources and algorithms for white-light fringe estimation at low light levels,” Appl. Opt. 41, 2655–2671 (2002). [CrossRef] [PubMed]
  6. K. Creath, “Phase-measurement interferometry techniques,” in Progress in Optics, E. Wolf, ed. (Pergamon, London, 1988), Vol. XXVI, pp. 349–393.
  7. M. M. Colavita, J. K. Wallace, B. E. Hines, Y. Gursel, F. Malbet, D. L. Palmer, X. P. Pan, M. Shao, J. W. Yu, A. F. Boden, P. J. Dumont, J. Gubler, C. D. Koresko, S. R. Kulkarni, B. F. Lane, D. W. Mobley, G. T. van Belle, “The Palomar Testbed Interferometer,” Astrophys. J. 510, 505–521 (1999). [CrossRef]
  8. M. Shao, M. M. Colavita, B. E. Hines, D. H. Staelin, D. J. Hutter, K. J. Johnston, D. Mozurkewich, R. S. Simon, J. L. Hershey, J. A. Hughes, G. H. Kaplan, “The Mark III stellar interferometer,” Astron. Astrophys. 193, 357–371 (1988).
  9. M. Shao, M. M. Colavita, “Long-baseline optical and infrared stellar interferometry,” Astron. Astrophys. 30, 457–498 (1992). [CrossRef]
  10. M. Shao, M. M. Colavita, “Potential of long-baseline infrared interferometry for narrow-angle interferometry,” Astron. Astrophys. 262, 353–358 (1992).
  11. M. M. Colavita, “Fringe visibility estimators for the Palomar Testbed interferometer,” Publ. Astron. Soc. Pac. 111, 111–117 (1999). [CrossRef]
  12. A. F. Boden, “SIM astrometric grid simulation development and performance assessment,” JPL Interoffice Memo. 10-005 (Jet Propulsion Laboratory, Pasadena, Calif., 1997).
  13. R. Swartz, “Metrology breaks and the SIM astrometric grid,” JPL Interoffice Memo. 17-063 (Jet Propulsion Laboratory, Pasadena, Calif., 2000).
  14. J. W. Goodman, Statistical Optics (Wiley, New York, 1985).
  15. W. J. Tango, R. Q. Twiss, “Michelson stellar interferometry,” in Progress in Optics, E. Wolf, ed. (Pergamon, London, 1980), Vol. XVII, pp. 239–277.
  16. J. E. Greivenkamp, “Generalized data reduction for heterodyne interferometry,” Opt. Eng. 23, 350–352 (1984). [CrossRef]
  17. P. R. Lawson, “Phase and group delay estimation,” in Principles of Long Baseline Stellar Interferometry, P. R. Lawson, ed., JPL Publ. 00-009 (Jet Propulsion Laboratory, Pasadena, Calif., 2000).
  18. J. T. Armstrong, D. Mozurkewich, L. J. Rickard, D. J. Hutter, J. A. Benson, P. F. Bowers, N. M. Elias, C. A. Hummel, K. J. Johnston, D. F. Buscher, J. H. Clark, L. Ha, L.-C. Ling, N. M. White, R. S. Simon, “The Navy Prototype Optical Interferometer,” Astrophys. J. 496, 550–571 (1998). [CrossRef]
  19. T. A. ten Brummelaar, “Correlation measurement and group delay tracking in optical stellar interferometry with a noisy detector,” Mon. Notes R. Astron. Soc. 285, 135–150 (1997). [CrossRef]
  20. M. Milman, J. Catanzarite, S. G. Turyshev, “The effect of wavenumber error on the computation of path-length delay in white-light interferometry,” Appl. Opt. 41, 4884–4890 (2002). [CrossRef] [PubMed]
  21. Note that, by taking the limit v → 0 in Eq. (6) [i.e., sinc(½ kvΔτi) → 1], one recovers the case of stepping OPD modulation with the familiar simple form of an observational equation: ℐi(k) = ℐ0[1 + V sin(ϕ0 + kxi)].

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited